A Computationally Efficient Approach to Nonlinear Control and Estimation of a Slider-to-Gimbal Platform

Abstract

This paper introduces a novel control and estimation approach for a Slider-to-Gimbal platform, combining discrete-time feedback linearization with an Unscented Kalman Filter achieving real-time state estimation. The proposed framework handles complex nonlinear dynamics, center of gravity fluctuations, and strict constraints of real-time operation. In contrast to continuous-time controllers demanding huge computational power, the discrete-time feedback linearization ensures robust stability. Additionally, the presented work reduces sensor reliance by employing the UKF which decreases sensor interference and estimates velocities and the center of gravity from only position and orientation data. The experiments are performed in MATLAB/Simulink, with tests spanning multiple reference trajectories, sensor arrangements (2-3 sensor utilization), and sampling periods (0.1 to 0.0001). Tracking errors for slider position, pan, and tilt angles reach as low as 0.0286 m, 0.0887 rad, and 0.1925 rad, respectively. Even utilizing only two sensors, errors are lower than 0.0275 m, 0.0894 rad, and 0.1756 rad, proving the method's robustness. Furthermore, the force and torque remain within practical limits to be utilized in real time applications. A minimum sampling interval of 0.0001 s produces the highest accuracy, while 0.01 s interval offers a balanced compromise between performance and computational effort. The results demonstrate that the proposed methodology is the candidate for real time application in appropriate with applicable control and sensor signals.